Differentially-rotating neutron star models with a parametrized rotation profile

Abstract

We analyze the impact of the rotation law on equilibrium sequences of relativistic differentially-rotating neutron stars in axisymmetry. The maximum allowed mass for each model is strongly affected by the distribution of the angular velocity in the radial direction and by the consequent degree of differential rotation. To study the wide parameter space implied by the choice of the rotation law, we introduce a functional form that generalizes the so-called "j-const. law" adopted in all previous work. We compute equilibrium sequences of differentially rotating stars with a polytropic equation of state starting from the spherically symmetric static case. By analyzing the sequences with decreasing degrees of differential rotation, we find that the maximum value of the ratio T/|W| of rotational kinetic energy to gravitational binding energy, is substantially limited in these cases to a value of 0.128.

R -mode frequencies of rapidly and differentially rotating relativistic neutron stars

“…law derived by [25,26], that has been widely used in the literature. (For more general rotation laws, see [27,28].) In the Newtonian limit, the j-const.…”

General-relativistic Rotation Laws in Rotating Fluid Bodies: Constant Linear Velocity

“…The angular momentum per unit mass j can be any function of r, where r is the distance from a (fixed) rotation axis. In contrast to that, in general relativity had been known only two families of rotation laws-one with j being a linear function of the angular velocity Ω [1][2][3] and a more recent nonlinear angular velocity proposal [4]. Their Newtonian limits recover only a small fraction of the set of Newtonian rotation curves.…”

General-relativistic rotation laws in rotating fluid bodies

“…In the Newtonian limit and large A one arrives at the rigid rotation, Ω = Ω c , while for small A one gets the constant angular momentum per unit mass. A three-parameter expression for j is proposed in [2]. Below we define a new family of rotation laws,…”

“…In contrast to that, for a long time the only known rotation law in general-relativistic hydrodynamics had been that with j as a linear function of the angular velocity. Recently Galeazzi, Yoshida and Eriguchi [2] have found a nonlinear angular velocity profile, that may approximate the Newtonian monomial rotation curves Ω 0 = w/r λ in the nonrelativistic limit. In this paper we define general-relativistic rotation curves j = j(Ω) that in the nonrelativistic limit exactly coincide with Ω 0 = w/r λ (0 ≤ λ ≤ 2, λ = 1).…”